Numerical simulation of acoustic holography with propagator adaptation: Application to a 3D disc

Acoustical holography can be used to identify the vibration velocity of an extended vibrating body. Such an inverse problem relies on the radiated acoustic pressure measured by a microphone array and on an a priori knowledge of the way the body radiates sound. Any perturbation on the radiation model leads to a perturbation on the velocity identified by the inversion process. Thus, to obtain the source vibration velocity with a good precision, it is useful to identify also an appropriate propagation model. Here, this identification, or adaptation, procedure rests on a geometrical interpretation of the acoustic holography in the objective space (here the radiated pressure space equipped with the L²-norm) and on a genetic algorithm.The propagator adaptation adds information to the holographic process, so it is not a regularisation method, which approximates the inverse of the model but does not affect the model. Moreover regularisations act in the variables space, here the velocities space. It is shown that an adapted model significantly decreases the quantity of regularisation needed to obtain a good reconstructed velocity, and that model adaptation improves significantly the acoustical holography results.In the presence of perturbations on the radiated pressure, some indications will be given on the interest or not to adapt the model, again thanks to the geometrical interpretation of holography in the objective space.As a numerical example, a disc whose vibration velocity on one of its sides is identified by acoustic holography is presented. On an industrial scale, this problem occurs due to the noise radiated by car wheels. The assessment of the holographic results has not yet been rigorously performed in such situations due to the complexity of the wheel environment made up of the car body, road and rolling conditions.